# 3D Surface Plotter - Graph z = f(x, y) Online with Rotation, Contours and PNG Export

> Free online 3D surface plotter: type z = f(x, y) and drag to rotate a height-coloured surface — solid, wireframe or contour, several at once, with PNG export.

- URL: https://qilingtools.com/en/math/3d-graph
- Category: Math Tools (https://qilingtools.com/en/math)
- Tags: [Math](https://qilingtools.com/en/tags/math), [Education](https://qilingtools.com/en/tags/education), [Charts & Visualization](https://qilingtools.com/en/tags/chart)
- Last updated: 2026-10-26
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

The graph of a two-variable function z = f(x, y) is a surface, and its shape is hard to picture from the formula alone. Type the formula and the tool samples it on a grid over your x and y ranges and draws a height-coloured 3D surface you can view from any angle. Switch to contours to see level curves on the surface and projected onto the floor. It is the 3D companion of the 2D function grapher — handy for multivariable calculus, partial derivatives, extrema and saddle points, or for illustrating slides.

## How to use

1. Type the formula after “z =”, e.g. sin(x)*cos(y) or x^2-y^2
2. Set the x and y ranges and the grid resolution (the z range is automatic)
3. Drag to rotate, scroll or pinch to zoom, and switch between solid, wireframe and contours
4. Add a second or third surface to compare, then export a PNG

## Features

- Same syntax as the 2D grapher: implicit multiplication, ^ for powers, sin cos exp ln sqrt and more
- Drag or swipe to rotate, wheel or pinch to zoom, one-click top / front / iso views and auto-rotate
- Shaded solid, wireframe with hidden lines removed, and contours with a projection on the floor
- Height colouring with five colour maps (viridis, plasma…) and a colour bar
- Up to four surfaces at once, each with its own visibility toggle
- The automatic z range clips spikes such as 1/r, or set it yourself
- Grid resolution from 10×10 to 120×120, still smooth to rotate at 60×60
- Presets: saddle, ripple sin(r)/r, paraboloid, monkey saddle, Gaussian bell, peaks and more
- Export a double-resolution PNG; everything is computed locally in your browser

## FAQ

### How do I enter a function of x and y?

Type only the right-hand side, e.g. x^2+y^2, sin(x)*cos(y) or exp(-(x^2+y^2)). You can drop the multiplication sign in 2x (but write 3x*y for 3xy), use ^ for powers, and functions such as sin, cos, tan, exp, ln, sqrt and abs plus the constants pi and e — the same syntax as the 2D grapher.

### Why does my surface have holes?

Either the function is undefined there (sin(r)/r at the origin, ln of a negative number) or the values fall outside the z range. The automatic z range cuts off spikes that shoot to infinity, like 1/r, so the rest of the surface is not flattened; enter a larger z range to see the whole spike.

### What is the difference between a saddle and a monkey saddle?

The saddle z = x² − y² has a minimum along x and a maximum along y at the origin — the textbook saddle point. The monkey saddle z = x³ − 3xy² has three downward directions (two legs and a tail) and all its second derivatives vanish at the origin, so the second-derivative test cannot classify it.

### What does the contour view show?

Contours join points of equal height, just like the lines on a topographic map: where they bunch together the surface is steep. The tool draws coloured contours on the surface and projects them onto the floor, which makes extrema, saddle points and the direction of the gradient easy to spot.

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